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The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty by Sam L. Savage

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CHAPTER 32
The DNA of Supply Chains
Recall the perishable antibiotic inventory example at the beginning of the book. This is, in effect, the DNA of all inventory problems. Think of it as a single link in the supply chain. Management scientists call it the Newsboy Problem, because it is analogous to the dilemma faced by someone purchasing newspapers for a particular day’s uncertain demand. If demand is less than the number of papers purchased, the excess will be wasted, whereas demand greater than the number on hand results in lost sales. In the case of the pharmaceutical firm, too much inventory resulted in a $50-per-unit spoilage cost, and too little inventory required paying air freight charges of $150 for each unit that they were short.
Suppose the average demand was five. If the firm kept five units in stock and if the demand actually was five, the cost would be zero because there is no penalty. When I falsely claim in class that zero is therefore the average cost, nearly all of my university and executive education students dutifully nod their heads in agreement.
But the graph of operating cost versus demand (Figure 32.1) makes it clear that a deviation of demand either way from the average of five results in a penalty, so average cost must be greater than zero. But how much greater?
We need the distribution of antibiotic demand to find out. Suppose that demand fluctuates from month to month with no systematic seasonality. Then Figure 32.2, the histogram of 36 months of ...

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